Senate Minority Leader Mitch McConnell (R., Ky.) and his wife, Elaine Chao, arrive for a victory celebration following the early results of the state Republican primary May 20, 2014 in Louisville.

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After years of missteps, Republicans are now picking the most-electable GOP candidates in their primaries, Senate Minority Leader Mitch McConnell said a day after winning his own primary election.

“Even if you have some back-and-forth during the primaries, I think what you’re going to see is a very unified right-of-center bloc with highly credible candidates going into the November election all across America,” the Kentucky Republican told reporters on Wednesday. “That’s not always [been] the case in the last two cycles, but I think it’s clearly the case this time.”

On Tuesday night, Mr. McConnell easily defeated conservative primary challenger Matt Bevin, winning 60% of the vote, compared with 36% for his rival. Candidates backed by business groups also prevailed over tea party opponents in primaries held for the Georgia and Oregon Senate races and an Idaho House GOP incumbent fended off a conservative challenge.

Mr. McConnell noted that after the polls closed Tuesday night, the conservative groups who had supported his GOP rival in the primary endorsed him in the general election. In November, he will face Kentucky Secretary of State Alison Lundergan Grimes, who easily won the Democratic primary.

“Collectively this group spent about $1 million against me in the primary, but they all got on board last night,” Mr. McConnell said. “Everybody wants to win.”

Republicans need to pick up a net six seats to reclaim the Senate majority.

Looking ahead to his tight race in the general election, Mr. McConnell said the primary returns underscored his state’s resistance to Democratic energy policy.

“There were 21 counties in which I got a bigger percentage of my primary vote than she got of hers,” he said. “What did those counties have in common? Almost every one of them was a coal county.”

The Grimes campaign did not immediately respond to a request for comment. However, on her website, Ms. Grimes said she opposes “President Obama’s attack on Kentucky’s energy industry” and has criticized regulations for threatening energy development in the state.

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